Majority logic gate based and-or-invert logic gate with non-linear input capacitors

ABSTRACT

A new class of logic gates are presented that use non-linear polar material. The logic gates include multi-input majority gates. Input signals in the form of digital signals are driven to non-linear input capacitors on their respective first terminals. The second terminals of the non-linear input capacitors are coupled a summing node which provides a majority function of the inputs. The majority node is then coupled driver circuitry which can be any suitable logic gate such as a buffer, inverter, NAND gate, NOR gate, etc. In the multi-input majority or minority gates, the non-linear charge response from the non-linear input capacitors results in output voltages close to or at rail-to-rail voltage levels. Bringing the majority output close to rail-to-rail voltage eliminates the high leakage problem faced from majority gates formed using linear input capacitors.

CLAIM OF PRIORITY

This application is a continuation of, and claims the benefit ofpriority to U.S. patent application Ser. No. 17/327,614, filed on May21, 2021, titled “MAJORITY LOGIC GATE WITH NON-LINEAR INPUT CAPACITORS”,and which is incorporated by reference in entirety.

BACKGROUND

Typical logic gates such as an AND gate, an OR gate, or a logic gatethat receives three or more inputs may consist of nine more transistorsper logic gate and many interconnects to connect the varioustransistors. As the number of transistors increases, power consumptionalso increases. As devices are pushing down the power envelope to savebattery power, existing circuit architecture for multi-input logic gatespresent challenges to the goal of lower power consumption.

The background description provided here is for the purpose of generallypresenting the context of the disclosure. Unless otherwise indicatedhere, the material described in this section is not prior art to theclaims in this application and are not admitted to be prior art byinclusion in this section.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the disclosure will be understood more fully from thedetailed description given below and from the accompanying drawings ofvarious embodiments of the disclosure, which, however, should not betaken to limit the disclosure to the specific embodiments, but are forexplanation and understanding only.

FIG. 1 illustrates a 3-input majority gate using linear input capacitorsresulting in non-rail-to-rail voltage swing at an input of a driver andleakage through the driver.

FIG. 2 illustrates a timing diagram showing operation of 3-inputmajority gate of FIG. 1 resulting in high static leakage.

FIG. 3 illustrates a plot showing charge transfer function fornon-linear capacitors compared to a linear capacitor.

FIG. 4 illustrates a 3-input majority gate using non-linear inputcapacitors, in accordance with some embodiments.

FIG. 5 illustrates a 3-input majority gate using non-linear inputcapacitors and no driver circuitry, in accordance with some embodiments.

FIG. 6 illustrates a set of plots showing logic state separation fornon-linear capacitors compared to a linear capacitor, in accordance withsome embodiments.

FIG. 7A illustrates a timing diagram for a 3-input majority or minoritygate using ferroelectric input capacitors, in accordance with someembodiments.

FIG. 7B illustrates a timing diagram from a 3-input majority gate orminority gate using paraelectric input capacitors, in accordance withsome embodiments.

FIG. 8 illustrates a 2-input AND or NAND gate using non-linear inputcapacitors, in accordance with some embodiments.

FIG. 9 illustrates a 2-input OR or NOR gate using non-linear inputcapacitors, in accordance with some embodiments.

FIG. 10 illustrates a majority gate based XOR gate using non-linearinput capacitors, in accordance with some embodiments.

FIG. 11 illustrates a majority gate based XOR gate using non-linearinput capacitors and with output driver, in accordance with someembodiments.

FIG. 12 illustrates a majority gate based complex logic gate withnon-linear input capacitors, in accordance with some embodiments.

FIG. 13 illustrates top down layout and corresponding cross-section of a3-input majority gate, respectively, in accordance with someembodiments.

FIGS. 14A-C illustrate a 2-input AND (or NAND) gate comprising twonon-linear capacitors, associated timing diagram, and associatedcharges, in accordance with some embodiments.

FIG. 15 illustrates a complex logic gate implemented using a 5-inputmajority gate, in accordance with some embodiments.

FIG. 16 illustrates a system-on-chip (SOC) that uses the majority logicgates having non-linear input capacitors, in accordance with someembodiments.

DETAILED DESCRIPTION

Some embodiments describe a new class of logic gates that use non-linearpolar material. The logic gates include multi-input majority or minoritygates. Input signals in the form digital signals are driven to firstterminals of capacitors with non-linear polar material. The secondterminals of the capacitors with non-linear polar material are coupledto form a majority node (or a summing node). Majority function of theinput signals occurs on this node. The majority node is then coupled toa capacitive node or device such as a gate terminal of a transistor. Invarious embodiments, this capacitive node is connected to a logic gatesuch as a CMOS circuitry, buffer, inverter, NAND gate, NOR gate,multiplexer, XOR gate, etc. The output of the logic can be used to driveadditional multi-input majority or minority gates or to devices of othertypes of transistor technologies. The logic gate can be implemented inany suitable technology such as complementary metal oxide semiconductor(CMOS), tunneling field effect transistor (TFET), GaAs basedtransistors, bipolar junction transistors (BJTs), Bi-CMOS transistors,etc. As such, majority or minority gate of various embodiments can becombined with existing transistor technologies. In various embodiments,the summing node or the majority node has a signal which reachesrail-to-rail (e.g., from ground to Vdd) resulting in lower leakage inthe subsequent logic gate. One drawback of using linear inputcapacitors, as opposed to non-linear input capacitors, is that thevoltage on the summing node or majority output node does not reachrail-to-rail voltage, resulting in high leakage in the output driver orlogic gate. Such issues are resolved by the multi-input majority orminority gates of various embodiments. In the multi-input majority orminority gates of various embodiments the non-linear charge responsefrom the non-linear input capacitors results in output voltages close torail-to-rail. Bringing the majority output close to rail-to-rail voltageeliminates the high leakage problem faced from majority gates formedusing linear input capacitors.

There are many technical effects of the various embodiments. Forexample, extremely compact basic logic gates are formed using non-linearcapacitors. The non-linear capacitors comprise non-linear polar materialthat can be ferroelectric material, para-electric material, ornon-linear dielectric. The logic gates of various embodiments become thebasis of adders, multipliers, sequential circuits, and other complexcircuits, etc. The majority gate of various embodiments lowers the powerconsumption because they do not use switching transistors and theinterconnect routings are much fewer than the interconnect routings usedin transitional CMOS logic gates. For example, 10× fewer interconnectlength is used by the majority gate of various embodiments thantraditional CMOS circuits for the same function and performance. Thecapacitors with non-linear polar material provide non-volatility thatallows for intermittent operation and zero power drain when not in use.

For example, a processor having such logic gates can enter and exitvarious types of low power states without having to worry about losingdata. Since the capacitor with non-linear polar material can storecharge from low energy devices, the entire processor can operate at muchlower voltage level from the power supply, which reduces overall powerof the processor. Further, very low voltage switching (e.g., 100 mV) ofthe non-linear polar material state allows for low swing signalswitching, which in turn results in low power.

The capacitors with non-linear polar material can be used with any typeof transistor. For example, the capacitors with non-linear polarmaterial of various embodiments can be used with planar or non-planartransistors. The transistors can be formed in the frontend or backend ofa die. The capacitors with non-linear polar material can be formed inthe frontend or backend of the die. As such, the logic gates can bepacked with high density compared to traditional logic gates. Othertechnical effects will be evident from the various embodiments andfigures.

In the following description, numerous details are discussed to providea more thorough explanation of embodiments of the present disclosure. Itwill be apparent, however, to one skilled in the art, that embodimentsof the present disclosure may be practiced without these specificdetails. In other instances, well-known structures and devices are shownin block diagram form, rather than in detail, in order to avoidobscuring embodiments of the present disclosure.

Note that in the corresponding drawings of the embodiments, signals arerepresented with lines. Some lines may be thicker, to indicate moreconstituent signal paths, and/or have arrows at one or more ends, toindicate primary information flow direction. Such indications are notintended to be limiting. Rather, the lines are used in connection withone or more exemplary embodiments to facilitate easier understanding ofa circuit or a logical unit. Any represented signal, as dictated bydesign needs or preferences, may actually comprise one or more signalsthat may travel in either direction and may be implemented with anysuitable type of signal scheme.

The term “device” may generally refer to an apparatus according to thecontext of the usage of that term. For example, a device may refer to astack of layers or structures, a single structure or layer, a connectionof various structures having active and/or passive elements, etc.Generally, a device is a three-dimensional structure with a plane alongthe x-y direction and a height along the z direction of an x-y-zCartesian coordinate system. The plane of the device may also be theplane of an apparatus, which comprises the device.

Throughout the specification, and in the claims, the term “connected”means a direct connection, such as electrical, mechanical, or magneticconnection between the things that are connected, without anyintermediary devices.

The term “coupled” means a direct or indirect connection, such as adirect electrical, mechanical, or magnetic connection between the thingsthat are connected or an indirect connection, through one or morepassive or active intermediary devices.

The term “adjacent” here generally refers to a position of a thing beingnext to (e.g., immediately next to or close to with one or more thingsbetween them) or adjoining another thing (e.g., abutting it).

The term “circuit” or “module” may refer to one or more passive and/oractive components that are arranged to cooperate with one another toprovide a desired function.

The term “signal” may refer to at least one current signal, voltagesignal, magnetic signal, or data/clock signal. The meaning of “a,” “an,”and “the” include plural references. The meaning of “in” includes “in”and “on.”

Here, the term “analog signal” generally refers to any continuous signalfor which the time varying feature (variable) of the signal is arepresentation of some other time varying quantity, i.e., analogous toanother time varying signal.

Here, the term “digital signal” generally refers to a physical signalthat is a representation of a sequence of discrete values (a quantifieddiscrete-time signal), for example of an arbitrary bit stream, or of adigitized (sampled and analog-to-digital converted) analog signal.

The term “scaling” generally refers to converting a design (schematicand layout) from one process technology to another process technologyand subsequently being reduced in layout area. The term “scaling”generally also refers to downsizing layout and devices within the sametechnology node. The term “scaling” may also refer to adjusting (e.g.,slowing down or speeding up—i.e. scaling down, or scaling uprespectively) of a signal frequency relative to another parameter, forexample, power supply level.

The terms “substantially,” “close,” “approximately,” “near,” and“about,” generally refer to being within +/−10% of a target value. Forexample, unless otherwise specified in the explicit context of theiruse, the terms “substantially equal,” “about equal” and “approximatelyequal” mean that there is no more than incidental variation betweenamong things so described. In the art, such variation is typically nomore than +/−10% of a predetermined target value.

Unless otherwise specified the use of the ordinal adjectives “first,”“second,” and “third,” etc., to describe a common object, merelyindicate that different instances of like objects are being referred to,and are not intended to imply that the objects so described must be in agiven sequence, either temporally, spatially, in ranking or in any othermanner

For the purposes of the present disclosure, phrases “A and/or B” and “Aor B” mean (A), (B), or (A and B). For the purposes of the presentdisclosure, the phrase “A, B, and/or C” means (A), (B), (C), (A and B),(A and C), (B and C), or (A, B and C).

The terms “left,” “right,” “front,” “back,” “top,” “bottom,” “over,”“under,” and the like in the description and in the claims, if any, areused for descriptive purposes and not necessarily for describingpermanent relative positions. For example, the terms “over,” “under,”“front side,” “back side,” “top,” “bottom,” “over,” “under,” and “on” asused herein refer to a relative position of one component, structure, ormaterial with respect to other referenced components, structures ormaterials within a device, where such physical relationships arenoteworthy. These terms are employed herein for descriptive purposesonly and predominantly within the context of a device z-axis andtherefore may be relative to an orientation of a device. Hence, a firstmaterial “over” a second material in the context of a figure providedherein may also be “under” the second material if the device is orientedupside-down relative to the context of the figure provided. In thecontext of materials, one material disposed over or under another may bedirectly in contact or may have one or more intervening materials.Moreover, one material disposed between two materials may be directly incontact with the two layers or may have one or more intervening layers.In contrast, a first material “on” a second material is in directcontact with that second material. Similar distinctions are to be madein the context of component assemblies.

The term “between” may be employed in the context of the z-axis, x-axisor y-axis of a device. A material that is between two other materialsmay be in contact with one or both of those materials, or it may beseparated from both of the other two materials by one or moreintervening materials. A material “between” two other materials maytherefore be in contact with either of the other two materials, or itmay be coupled to the other two materials through an interveningmaterial. A device that is between two other devices may be directlyconnected to one or both of those devices, or it may be separated fromboth of the other two devices by one or more intervening devices.

Here, multiple non-silicon semiconductor material layers may be stackedwithin a single fin structure. The multiple non-silicon semiconductormaterial layers may include one or more “P-type” layers that aresuitable (e.g., offer higher hole mobility than silicon) for P-typetransistors. The multiple non-silicon semiconductor material layers mayfurther include one or more “N-type” layers that are suitable (e.g.,offer higher electron mobility than silicon) for N-type transistors. Themultiple non-silicon semiconductor material layers may further includeone or more intervening layers separating the N-type from the P-typelayers. The intervening layers may be at least partially sacrificial,for example to allow one or more of a gate, a source, or a drain to wrapcompletely around a channel region of one or more of the N-type andP-type transistors. The multiple non-silicon semiconductor materiallayers may be fabricated, at least in part, with self-aligned techniquessuch that a stacked CMOS device may include both a high-mobility N-typeand P-type transistor with a footprint of a single FET (field effecttransistor).

Here, the term “backend” generally refers to a section of a die which isopposite of a “frontend” and where an IC (integrated circuit) packagecouples to IC die bumps. For example, high-level metal layers (e.g.,metal layer 6 and above in a ten-metal stack die) and corresponding viasthat are closer to a die package are considered part of the backend ofthe die. Conversely, the term “frontend” generally refers to a sectionof the die that includes the active region (e.g., where transistors arefabricated) and low-level metal layers and corresponding vias that arecloser to the active region (e.g., metal layer 5 and below in theten-metal stack die example).

It is pointed out that those elements of the figures having the samereference numbers (or names) as the elements of any other figure canoperate or function in any manner similar to that described, but are notlimited to such.

FIG. 1 illustrates 3-input majority gate 100 using linear inputcapacitors resulting in non-rail-to-rail voltage swing at an input of adriver and leakage through the driver. 3-input majority gate 100 is atypical majority gate that uses linear input capacitors C1, C2, and C3that are coupled to inputs a, b, and c, respectively, on one end and toa summing node n1 on another end. The summing node is where the majorityfunction is performed e.g., Majority(a,b,c). The voltage developed onnode n1 is then used to drive a CMOS driver 101. If CMOS driver 101 isan inverter, the output “out” provides a minority function of the inputse.g., Minority(a,b,c). Here, the voltage developed on node n1 is notrail-to-rail voltage. As a result, standby current rushes through driver101 because some of its transistors are not fully off due to thenon-rail-to-rail voltage on node n1. As such, energy is wasted and3-input majority gate 100 becomes unsuitable gate for use in any lowpower applications.

FIG. 2 illustrates timing diagram 200 showing operation of 3-inputmajority gate of FIG. 1 resulting in high static leakage. Timing diagram200 shows digital input signals for inputs a, b, and c. Depending on thelogic levels of inputs a, b, and c, a voltage is developed on summingnode n1. This voltage is illustrated by waveform Maj(a,b,c). The voltagedriven by inverter 101 on node “out” is the minority output, Min(a,b,c).The last waveform in the stack of waveforms shows the impact of usinglinear input capacitors as the basis of performing a majority function.When the voltage on node n1 is between Vdd and ground, crowbar current(also referred to as standby current) passes through the supply rail tothe ground in CMOS driver 101. This crowbar current is substantiallylarger than leakage current (e.g., current through CMOS driver 101 whenall its devices are off). As a result, 3-input majority gate 100 becomesunsuitable gate for use in any low power applications.

FIG. 3 illustrates a set of plots showing charge transfer function fornon-linear capacitors compared to a linear capacitor. Plot 300 comparesthe transfer function for a linear capacitor, a paraelectric capacitor(a non-linear capacitor) and a ferroelectric capacitor (a non-linearcapacitor). Here, x-axis is input voltage or voltage across thecapacitor, while the y-axis is the charge on the capacitor. Plot 320shows the charge and voltage relationship for a ferroelectric capacitor.A capacitor with ferroelectric material (also referred to as a FEC) is anon-linear capacitor with its potential V_(F)(Q_(F)) as a cubic functionof its charge. Plot 320 illustrates characteristics of a FEC. Plot 320is a charge-voltage (Q-V) plot for a block of Pb(Zr_(0.5)Ti_(0.5))O₃ ofarea (100 nm)² and thickness 20 nm (nanometer). Plot 320 shows localextrema at +/−V_(o) indicated by the dashed lines. Here, the term V_(c)is the coercive voltage. In applying a potential V across the FEC, itscharge can be unambiguously determined only for |V|>V_(o). Otherwise,the charge of the FEC is subject to hysteresis effects.

FIG. 4 illustrates 3-input majority gate 400 using non-linear inputcapacitors, in accordance with some embodiments. In some embodiments,3-input majority gate 400 comprises non-linear input capacitors C1 n 1,C2 n 1, and C3 n 1 that receives digital signals a, b, and c,respectively. Here, signal names and node names are interchangeablyused. For example, ‘a’ refers to node ‘a’ or signal ‘a’ depending on thecontext of the sentence. One end or terminal of capacitor C1 n 1 iscoupled to node a while the other end of capacitor C1 n 1 is coupled tosumming node Vs. The same is true for other non-linear capacitors C2 n 1and C3 n 1 as shown. In some embodiments, 3-input majority gate 400comprises a driver circuitry 101. In this example, driver circuitry 101is an inverter. In other embodiments, other types of driver circuitriescan be used such as NAND gate, NOR gate, multiplexer, buffer, and otherlogic gates. The majority function is performed at summing node Vs asMajority(a,b,c). In this example, since driver 101 is an inverter,minority function is performed at output “out” as Minority(a,b,c).

In some embodiments, in addition to the gate capacitance of drivercircuitry 101, an additional linear capacitor CL is coupled to summingnode Vs and ground as shown. In some embodiments, this linear capacitorCL is a non-ferroelectric capacitor. In some embodiments, thenon-ferroelectric capacitor includes one of: dielectric capacitor,para-electric capacitor, or non-linear dielectric capacitor. Adielectric capacitor comprises first and second metal plates with adielectric between them. Examples of such dielectrics are: HfO, ABO3perovskites, nitrides, oxy-fluorides, oxides, etc. A para-electriccapacitor comprises first and second metal plates with a para-electricmaterial between them. In some embodiments, f-orbital materials (e.g.,lanthanides) are doped to the ferroelectric materials to makeparaelectric material. Examples of room temperature paraelectricmaterial include: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and y is0.95)), HfZrO2, Hf—Si—O, La-substituted PbTiO3, PMN-PT based relaxorferroelectrics. A dielectric capacitor comprises first and second metalplates with non-linear dielectric capacitor between them. The range fordielectric constant is 1.2 to 10000. The capacitor CL can be implementedas MIM (metal-insulator-metal) capacitor technology, transistor gatecapacitor, hybrid of metal capacitors or transistor capacitor. Thecapacitor CL can be implemented as MIM (metal-insulator-metal) capacitortechnology, transistor gate capacitor, or hybrid of metal capacitors ortransistor capacitor.

In some embodiments, the non-linear input capacitors C1 n 1, C2 n 1, andC3 n 1 comprise non-linear polar material. In some embodiments, thenon-linear polar material includes one of: ferroelectric (FE) material,para-electric material, relaxor ferroelectric, or non-linear dielectric.In various embodiments, para-electric material is the same as FEmaterial but with chemical doping of the active ferroelectric ion by anion with no polar distortion. In some cases, the non-polar ions arenon-s orbital ions formed with p, d, f external orbitals. In someembodiments, non-linear dielectric materials are same as para-electricmaterials, relaxors, and dipolar glasses.

In some embodiments, f-orbital materials (e.g., lanthanides) are dopedto the ferroelectric material to make paraelectric material. Examples ofroom temperature paraelectric material include: SrTiO3, Ba(x)Sr(y)TiO3(where x is −0.5, and y is 0.95), HfZrO2, Hf—Si—O, La-substitutedPbTiO3, and PMN-PT based relaxor ferroelectrics.

In various embodiments, the FE material can be any suitable low voltageFE material that allows the FE material to switch its state by a lowvoltage (e.g., 100 mV). In some embodiments, the FE material comprises aperovskite of the type ABO3, where ‘A’ and B′ are two cations ofdifferent sizes, and ‘0’ is oxygen which is an anion that bonds to boththe cations. Generally, the size of A atoms is larger than the size of Batoms. In some embodiments, the perovskite can be doped (e.g., by La orLanthanides). Perovskites can be suitably doped to achieve a spontaneousdistortion in a range of 0.3 to 2%. For example, for chemicallysubstituted lead titanate such as Zr in Ti site; La, Nb in Ti site, theconcentration of these substitutes is such that it achieves thespontaneous distortion in the range of 0.3 to 2%. For chemicallysubstituted BiFeO3, BiCrO3, BiCoO3 class of materials, La or rare earthsubstitution into the Bi site can tune the spontaneous distortion. Insome embodiments, perovskite includes one of: BaTiO3, PbTiO3, KNbO3, orNaTaO3.

Threshold in the FE material has a highly non-linear transfer functionin the polarization vs. voltage response. The threshold is related to:a) non-linearity of switching transfer function; and b) the squarenessof the FE switching. The non-linearity of switching transfer function isthe width of the derivative of the polarization vs. voltage plot. Thesquareness is defined by the ratio of the remnant polarization to thesaturation polarization; perfect squareness will show a value of 1.

The squareness of the FE switching can be suitably manipulated withchemical substitution. For example, in PbTiO3 a P-E(polarization-electric field) square loop can be modified by La or Nbsubstitution to create an S-shaped loop. The shape can be systematicallytuned to ultimately yield a non-linear dielectric. The squareness of theFE switching can also be changed by the granularity of the FE layer. Aperfect epitaxial, single crystalline FE layer will show highersquareness (e.g., ratio is closer to 1) compared to a poly crystallineFE. This perfect epitaxial can be accomplished by the use of latticematched bottom and top electrodes. In one example, BiFeO (BFO) can beepitaxially synthesized using a lattice matched SrRuO3 bottom electrodeyielding P-E loops that are square. Progressive doping with La willreduce the squareness.

In some embodiments, the FE material is contacted with a conductivemetal oxide that includes one of the conducting perovskite metallicoxides exemplified by: La—Sr—CoO3, SrRuO3, La—Sr—MnO3, YBa2Cu3O7,Bi2Sr2CaCu2O8, LaNiO3, and ReO3.

In some embodiments, the FE material comprises a stack of layersincluding low voltage FE material between (or sandwiched between)conductive oxides. In various embodiments, when FE material is aperovskite, the conductive oxides are of the type AA′BB′O3. A′ is adopant for atomic site A, it can be an element from the Lanthanidesseries. B′ is a dopant for atomic site B, it can be an element from thetransition metal elements especially Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu,Zn. A′ may have the same valency of site A, with a differentferroelectric polarizability.

In some embodiments, the FE material comprises hexagonal ferroelectricsof the type h-RMnO3, where R is a rare earth element such as: cerium(Ce), dysprosium (Dy), erbium (Er), europium (Eu), gadolinium (Gd),holmium (Ho), lanthanum (La), lutetium (Lu), neodymium (Nd),praseodymium (Pr), promethium (Pm), samarium (Sm), scandium (Sc),terbium (Tb), thulium (Tm), ytterbium (Yb), and yttrium (Y). Theferroelectric phase is characterized by a buckling of the layered MnO5polyhedra, accompanied by displacements of the Y ions, which lead to anet electric polarization. In some embodiments, hexagonal FE includesone of: YMnO3 or LuFeO3. In various embodiments, when the FE materialcomprises hexagonal ferroelectrics, the conductive oxides adjacent tothe FE material are of A2O3 (e.g., In2O3, Fe2O3) and AB2O3 type, where‘A’ is a rare earth element and B is Mn.

In some embodiments, FE material comprises improper FE material. Animproper ferroelectric is a ferroelectric where the primary orderparameter is an order mechanism such as strain or buckling of the atomicorder. Examples of improper FE material are LuFeO3 class of materials orsuper lattice of ferroelectric and paraelectric materials PbTiO3 (PTO)and SnTiO3 (STO), respectively, and LaAlO3 (LAO) and STO, respectively.For example, a super lattice of [PTO/STO]n or [LAO/STO]n, where ‘n’ isbetween 1 to 100. While various embodiments here are described withreference to ferroelectric material for storing the charge state, theembodiments are also applicable for paraelectric material. For example,the capacitor of various embodiments can be formed using paraelectricmaterial instead of ferroelectric material.

In some embodiments, the FE material includes one of: Hafnium (Hf),Zirconium (Zr), Aluminum (Al), Silicon (Si), their oxides or theiralloyed oxides. In some embodiments, FE material includes one of:Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)N or Al(1−x−y)Mg(x)Nb(y)N, ydoped HfO2, where x includes one of: Al, Ca, Ce, Dy, Er, Gd, Ge, La, Sc,Si, Sr, Sn, or Y, wherein ‘x’ is a fraction. In some embodiments, the FEmaterial includes Bismuth ferrite (BFO), lead zirconate titanate (PZT),BFO with doping material, or PZT with doping material, wherein thedoping material is one of Nb or relaxor ferroelectrics such as PMN-PT.

In some embodiments, the FE material includes Bismuth ferrite (BFO), BFOwith a doping material where in the doping material is one of Lanthanum,or any element from the lanthanide series of the periodic table. In someembodiments, the FE material includes lead zirconium titanate (PZT), orPZT with a doping material, wherein the doping material is one of La,Nb. In some embodiments, the FE material includes a relaxorferro-electric including one of lead magnesium niobate (PMN), leadmagnesium niobate-lead titanate (PMN-PT), lead lanthanum zirconatetitanate (PLZT), lead scandium niobate (PSN), Barium Titanium-BismuthZinc Niobium Tantalum (BT-BZNT), or Barium Titanium-Barium StrontiumTitanium (BT-BST).

In some embodiments, the FE material includes Hafnium oxides of theform, Hf1−x Ex Oy where E can be Al, Ca, Ce, Dy, er, Gd, Ge, La, Sc, Si,Sr, Sn, or Y. In some embodiments, FE material 105 includes Niobate typecompounds LiNbO3, LiTaO3, Lithium iron Tantalum Oxy Fluoride, BariumStrontium Niobate, Sodium Barium Niobate, or Potassium strontiumniobate.

In some embodiments, the FE material comprises multiple layers. Forexample, alternating layers of [Bi2O2]2+, and pseudo-perovskite blocks(Bi4Ti3O12 and related Aurivillius phases), with perovskite layers thatare n octahedral layers in thickness can be used.

In some embodiments, the FE material comprises organic material. Forexample, Polyvinylidene fluoride or polyvinylidene difluoride (PVDF).The FE material is between two electrodes. These electrodes areconducting electrodes. In some embodiments, the electrodes areperovskite templated conductors. In such a templated structure, a thinlayer (e.g., approximately 10 nm) of a perovskite conductor (such asSrRuO3) is coated on top of IrO2, RuO2, PdO2, or PtO2 (which have anon-perovskite structure but higher conductivity) to provide a seed ortemplate for the growth of pure perovskite ferroelectric at lowtemperatures. In some embodiments, when the ferroelectric compriseshexagonal ferroelectric material, the electrodes can have hexagonalmetals, spinels, or cubic metals. Examples of hexagonal metals include:PtCoO2, PdCoO2, and other delafossite structured hexagonal metallicoxides such as Al-doped ZnO. Examples of spinels include Fe3O4 andLiV2O4. Examples of cubic metals include Indium Tin Oxide (ITO) such asSn-doped In2O3.

The majority function is performed at the summing node Vs, and theresulting voltage is projected on to capacitance of driver circuitry101. For example, the majority function of the currents (I_(a), I_(b),and I_(c)) on node Vs results in a resultant current that chargescapacitor 105. Table 1 illustrates the majority function f(Majority a,b, c).

TABLE 1 a b c Vs (f(Majority a, b, c)) 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 1 10 0 0 1 0 1 1 1 1 0 1 1 1 1 1

The charge developed on node Vs produces a voltage and current that isthe output of the majority gate 400. Any suitable driver 101 can drivethis output. For example, a non-FE logic, FE logic, CMOS logic, BJTlogic, etc. can be used to drive the output to a downstream logic.Examples of the drivers include inverters, buffers, NAND gates, NORgates, XOR gates, amplifiers, comparators, digital-to-analog converters,analog-to-digital converters, multiplexers, etc.

While FIG. 4 illustrates a 3-input majority gate, the same concept canbe extended to more than 3 inputs to make an N-input majority gate,where N is greater than 2. In various embodiments, ‘N’ is an odd number.For example, a 5-input majority gate is similar to a input majority gate400 but for additional inputs ‘d’ and ‘e’. These inputs can come fromthe same drivers or from different drivers.

In some embodiments, the 3-input majority gate can be configured as afast inverter with a much faster propagation delay compared to a similarsized (in terms of area footprint) CMOS inverter. This is particularlyuseful when the inputs have a significantly slower slope compared to thepropagation delay through the non-linear input capacitors. One way toconfigurate the 3-input majority gate as an inverter is to set one inputto a logic high (e.g., b=1) and set another input to a logic low (e.g.,b=0). The third input is the driving input which is to be inverted. Theinversion will be at the Vs node. The same technique can also be appliedto N-input majority gate, where ‘N’ is 1 or any other odd number. In anN-input majority gate, (N−1)/2 inputs are set to ‘1’ and (N−1)/2 inputsare set to ‘0’, and one input is used to decide the inversion function.It will be appreciated that the various embodiments are described as amajority gate, the same concepts are applicable to a minority gate. In aminority gate the driving circuitry is an inverting circuitry coupled tothe summing node Vs. The minority function is seen at the output of theinverting circuitry.

In some embodiments, (2N−1) input majority gate can operate as anN-input AND gate where (N−1) inputs of the majority gate are set tozero. The AND function will be seen at the summing node Vs. Similarly,N-input NAND, OR, NOR gates can be realized. In various embodiments, thesumming node Vs is driven by a driver circuitry (e.g., inverter, buffer,NAND gate, AND gate, OR gate, NOR gate, or any other logic circuitry).However, driver circuitry 101 can be replaced with another majority orminority gate. In one such embodiment, the storage node Vs is directlycoupled to a non-linear capacitor of another majority or minority gate.

Any logic function ƒ(x₁, x₂, . . . x_(n)) can be represented by twolevels of logic as given by the min-term expansion:ƒ(x ₁ ,x ₂ , . . . x _(n))=V _(C) ₁ _(,C) ₂ _(, . . . ,C) _(n) ƒ(x ₁ ,x₂ , . . . x _(n))∧x ₁ ^(C) ¹ ∧x ₂ ^(C) ² ∧x ₃ ^(C) ³ . . . ∧x _(n) ^(C)^(n)where C_(i) is either 0 or 1. When C_(i) is 1, x_(i) ^(C) _(i)=x_(i)(the input is used in its original form). When C_(i) is 0, x_(i) ^(C)^(i) ′=x_(i) (the input is used in its inverted form). The first levelof logic is represented by at most 2^(n) AND gates (Δ), one for each ofthe 2^(n) possible combinations of 0 and 1 for C₁, C₂, . . . . C_(n).The second level of logic is represented by a single OR gate (∨). Eachoperand of the OR gate is a representation of a row in the truth tablefor ƒ(x₁, x₂, . . . x_(n)).

A (2N−1)-input majority gate can represent an N-input AND gate, by tying(N−1) of the majority gate's inputs to a ground level. Similarly, a(2N−1)-input majority gate can represent an N-input OR gate, by tying(N−1) of the majority gate's inputs to a supply level (Vdd). Since amajority gate can represent AND and OR gates, and the inputs to the ANDand OR gates are either original or inverted forms of the input digitalsignals, any logic function can be represented by majority gates andinverters only, in accordance with some embodiments.

FIG. 5 illustrates 3-input majority gate 500 using non-linear inputcapacitors and no driver circuitry, in accordance with some embodiments.In some embodiments, the summing node Vs is not coupled to a CMOS driver(e.g., buffer, inverter, NAND gate, or any other CMOS logic gate). Inone example, Vs is coupled to another majority or minority gate. Forinstance, Vs is coupled to a terminal of another non-linear capacitor ofanother majority or minority gate.

FIG. 6 illustrates a set of plots 600 and 620 showing logic stateseparation for non-linear capacitors compared to a linear capacitor, inaccordance with some embodiments. The sum of all charges must be zero todetermine Vs for given sets of inputs V_(a), V_(b), and V_(c) (which arevoltages on nodes a, b, and c, respectively) as follows:ΣQ(V _(s))=Q _(a)(V _(a) −V _(s))+Q _(b)(V _(b) −V _(s))+Q _(c)(V _(c)−V _(s))−C _(L) V _(s)=0

Plot 600 shows sum of charges for different values of V_(a), V_(b), andV_(c) when the input capacitors are linear capacitors as in FIG. 1. Plot620 shows sum of charges for different values of V_(a), V_(b), and V_(c)when the input capacitors are non-linear capacitors as in FIG. 4. Thedifferent values are: V_(a)=0, V_(b)=0, and V_(c)=0; V_(a)=1, V_(b)=0,and V_(c)=1; V_(a)=1, V_(b)=0, and V_(c)=0; and V_(a)=1, V_(b)=1, andV_(c)=1.

Plot 600 shows two points 601 and 602 for inputs (1,0,0) for (V_(a),V_(b), and V_(c)) and (1,1,0) which do not provide a clear logic levelof 0 or 1. Inputs (1,0,0) for (V_(a), V_(b), and V_(c)) are expected togenerate a 0 on node n1, but results in a higher voltage closer to 0.3,which is too close to a threshold voltage of transistor of drivercircuitry 101. Inputs (1,1,0) for (V_(a), V_(b), and V_(c)) are expectedto generate a 1 on node n1, but results in a lower voltage closer to0.7. Such voltages on node n1 result in crowbar current through drivercircuitry 101. Plot 620 shows the desired majority gate solution whereall input combinations result in clear voltage levels of 0 (e.g., 621)or 1 (622).

FIG. 7A illustrates timing diagram 700 for a 3-input majority orminority gate using ferroelectric input capacitors, in accordance withsome embodiments. FIG. 7B illustrates timing diagram 720 from a 3-inputmajority gate or minority gate using paraelectric input capacitors, inaccordance with some embodiments. In both cases, the voltage on node Vsshows a rail-to-rail voltage for majority function. Such rail-to-railvoltage suppresses crowbar current through driver circuitry 101. Forsome input combinations, using ferroelectric material can suppressleakage current below CMOS leakage level compared to using paraelectricmaterial for the input capacitors.

FIG. 8 illustrates a 2-input AND or NAND gate 800 using non-linear inputcapacitors, in accordance with some embodiments. Gate 800 is similar togate 400 but for providing a constant voltage to one of the inputs, hereinput ‘c’. When input ‘c’ is set to ground level (e.g., 0 V), themajority function on node Vs is an AND function of inputs a and b, andthe resulting output of inverter 101 is a NAND function of inputs a andb, in accordance with some embodiments.

FIG. 9 illustrates a 2-input OR or NOR gate 900 using non-linear inputcapacitors, in accordance with some embodiments. Gate 900 is similar togate 400 but for providing a constant voltage to one of the inputs, hereinput ‘c’. When input ‘c’ is set to supply level (e.g., Vdd), themajority function on node Vs is an OR function of inputs a and b, andthe resulting output of inverter 101 is a NOR function of inputs a andb, in accordance with some embodiments.

FIG. 10 illustrates a majority gate based XOR gate 1000 using non-linearinput capacitors, in accordance with some embodiments. XOR gate 1000 isa 2-input XOR gate that performs XOR function on inputs a and b. Invarious embodiments, XOR gate 1000 comprises non-linear input capacitorsC1 n 1, C2 n 1, C3 n 1, C4 n 1, C5 n 1, and C6 n 1, inverter 101, andnon-linear output capacitors C7 n 1, C8 n 1, and C9 n 1. Capacitors C1 n1, C2 n 1, and C3 n 1 receive inputs a, b, and 0, and perform majorityAND function on node Vs1 like AND gate 800. Capacitors C4 n 1, C5 n 1,and C6 n 1 receive inputs a, b, and Vdd, and perform majority ORfunction on node Vs2 like OR gate 900. The NAND output on node out1 isreceived by output capacitor C7 n 1. The OR output on node Vs2 isreceived by capacitor C8 n 1. Capacitor C9 n 1 receives a predeterminedinput 0 in this example. The majority function on node out3 is an AND ofout1, out2, and 0. In some embodiments, instead of driving voltage onnode Vs2 to out2, buffer 1001 is used between nodes Vs2 and out2. Insome embodiments, instead of driving output out3 as the XOR output,buffer 1002 is used to output the XOR output on node out. In someembodiments, Vs2 is directly connected to node out2. In someembodiments, out3 is directly connected to node out. In someembodiments, linear or non-linear capacitors CL1, CL2, and CL3 are addedon the summing nodes Vs1, Vs2, and out3, respectively. By swapping thevoltages ‘0’ and ‘Vdd’ different logic functions can be realized, inaccordance with various embodiments.

FIG. 11 illustrates a majority gate based XOR gate 1100 using non-linearinput capacitors and with output driver, in accordance with someembodiments. Compared to XOR gate 1000, here inverter 101 is removed andAND output on Vs1 is directly provided to capacitor C7 n 1. In thiscase, node out1 is shorted to node Vs1. In some embodiments, buffer 1101is used to drive the output on node Vs1 to node out1. In someembodiments, Vs2 node provides a majority OR function of inputs a and b.The result of majority OR is then inverted by inverter 1001 to generatea NOR function on node out2. Out2 then drives capacitors C8 n 1. In someembodiments, in input to capacitor C9 n 1 is Vdd. The function on nodeout3 is an OR function of out1 and out2, which is inverted by inverter1002 to generate the XOR logic. By swapping the voltages ‘0’ and ‘Vdd’different logic functions can be realized, in accordance with variousembodiments. In some embodiments, Vs2 is directly connected to nodeout2. In some embodiments, out3 is directly connected to node out.

FIG. 12 illustrates a majority gate based complex logic gate 1200 withnon-linear input capacitors, in accordance with some embodiments.Complex logic gate 1200 is configured as an And-Or-Invert (AOI) gate,which comprises non-linear input capacitors C1 n 1, C2 n 1, and C3 n 1coupled to inputs a, b, and 0, respectively. The summing node Vs1provides an AND function of inputs a and b. Gate 1200 further comprisesoutput non-linear capacitors C4 n 1, C5 n 1, and C6 n 1, and outputdriver (e.g., inverter 1202). In some embodiments, Vs1 is directlycoupled to node out1 (e.g., out1 and Vs1 are shorted together). In someembodiments, buffer 1201 drives the voltage on Vs1 to node ou1. In someembodiments, capacitor C4 n 1 receives input c while capacitor C6 n 1receives input Vdd. The function on node Vs2 is an OR of c and out1,which when inverted by inverter 1202 generates an AOI output on nodeout. By swapping the voltages ‘0’ and ‘Vdd’ different logic functionscan be realized, in accordance with various embodiments. For example,Or-AND-Inverter, 3-input NOR, 3-input NAND, etc. can be realized usinggate 1200. Compared to a CMOS AOI gate that uses at least 6 transistorsand is only able to do one function (AOI), here multiple functions canbe realized using 6 non-linear capacitors and 2 transistors (when buffer1201 is removed). In some embodiments, linear capacitors CL1 and CL2 areadded on the summing nodes to hold the voltage.

FIG. 13 illustrates top down layout and corresponding cross-section of a3-input majority gate, respectively, in accordance with someembodiments. Layout 1300 illustrates a compact layout of 3-inputmajority gate of FIG. 4 with a pitch of two minimum sized transistorsMNinv and MPinv of inverter 101. In some embodiments, non-linear inputcapacitors C1 n 1, C2 n 1, and C3 n 1 are positioned in the same set oflayers. For example, non-linear capacitors C1 n 1, C2 n 1, and C3 n 1are positioned in the place of via for metal layer 1 (M1) to metal layer2 (M2).

In some embodiments, transistors MNinv and MPinv are fabricated in thefrontend of the die. Inputs a, b, and c are on M2. Common node Vs (alsoreferred to as charge integration layer or node) is on M1. The commonnode Vs1 is shared by non-linear capacitors (C1 n 1, C2 n 1, and C3 n 1)and/or non-linear polar capacitor 105. While non-linear capacitors C1 n1, C2 n 1, and C3 n 1 are positioned in location of M1-via-M2, they canbe further located in the backend of the die. For example, non-linearcapacitors C1 n 1, C2 n 1, and C3 n 1, can be positioned in M4-Via-M5 orhigher. As such, lower metal layers are freed up for routing of othersignals.

Transistors MNinv and MPinv can be planar or non-planar transistors. Insome embodiments, transistors MNinv and MPinv can be formed in thefrontend or backend. In some embodiments, MNinv and MPinv are stackedtransistors. In some embodiments, one or more of non-linear capacitorsC1 n 1, C2 n 1, and C3 n 1, are formed in the frontend or backend. Thetransistors here can be Square Wire, Rectangular Ribbon Transistors,Gate All Around Cylindrical Transistors, Tunneling FETs ferroelectricFETs (FeFETs), bi-polar transistors (BJT), BiCMOS, or other devicesimplementing transistors functionality, for instance, carbon nanotubesor spintronic devices. In some embodiments, the transistors are typicalmetal oxide semiconductor (MOS) transistors or their derivativeincluding Tri-Gate and FinFET transistors. While MOSFET have symmetricalsource and drain terminals, TFET device has asymmetric source and drainterminals.

Transistors MNinv and MPinv are formed in/on substrate 1301, andcomprises respective source 1302, drain 1303, channel region 1304,source contact 1308 a, drain contact 1308 b, and gate comprising gatedielectric 1305, gate liners 1306 a and 1306 b; gate metal 1307.

Substrate 1301 includes a suitable semiconductor material such as:single crystal silicon, polycrystalline silicon and silicon on insulator(SOI). In one embodiment, substrate 1301 includes other semiconductormaterials such as: Si, Ge, SiGe, or a suitable group III-V or groupIII-N compound. Substrate 1301 may also include semiconductor materials,metals, dopants, and other materials commonly found in semiconductorsubstrates.

In some embodiments, source region 1302 and drain region 1303 for eachtransistor are formed within substrate 1301 adjacent to the gate stackof the transistor. In various embodiments, p-type transistors MPinv isformed in an n-well, which is in substrate 1301. The source region 1302and drain region 1303 are generally formed using either anetching/deposition process or an implantation/diffusion process.

In the etching and/or deposition process, substrate 1301 may first beetched to form recesses at the locations of the source 1302 and drain1303 regions. An epitaxial deposition process may then be carried out tofill the recesses with material that is used to fabricate the sourceregion 1302 and drain region 1303. In the implantation/diffusionprocess, dopants such as boron, aluminum, antimony, phosphorous, orarsenic may be ion-implanted into the substrate to form the sourceregion 1302 and drain region 1303. An annealing process that activatesthe dopants and causes them to diffuse further into substrate 1301typically follows the ion-implantation process.

In some embodiments, one or more layers of metal and/or metal alloys areused to form the source region 1302 and drain region 1303. In someembodiments, source region 1302 and drain region 1303 are formed usingone or more alternate semiconductor materials such as germanium or asuitable group III-V compound. In some embodiments, source region 1302and drain region 1303 are fabricated using a silicon alloy such assilicon germanium or silicon carbide. In some embodiments, theepitaxially deposited silicon alloy is doped in-situ with dopants suchas boron, arsenic, or phosphorous.

The semiconductor material for channel region 1304 may have the samematerial as substrate 1301 or n-well for a p-type transistor MPinv, inaccordance with some embodiments. In some embodiments, channel region604 includes one of: Si, SiGe, Ge, and GaAs.

The gate dielectric layer 1305 may include one layer or a stack oflayers. The one or more layers may include high-k dielectric material,silicon oxide, and/or silicon dioxide (SiO₂). The high-k dielectricmaterial may include elements such as: zinc, niobium, scandium, leanyttrium, hafnium, silicon, strontium, oxygen, barium, titanium,zirconium, tantalum, aluminum, and lanthanum. Examples of high-kmaterials that may be used in the gate dielectric layer include: leadzinc niobate, hafnium oxide, lead scandium tantalum oxide, hafniumsilicon oxide, yttrium oxide, aluminum oxide, lanthanum oxide, bariumstrontium titanium oxide, lanthanum aluminum oxide, titanium oxide,zirconium oxide, tantalum oxide, and zirconium silicon oxide. In someembodiments, when a high-k material is used, an annealing process isused on the gate dielectric layer 1305 to improve its quality.

In some embodiments, a pair of liner layers (sidewall liners) 606 a/bare formed on opposing sides of the gate stack that bracket the gatestack. The pair of liner layers 1306 a/b are formed from a material suchas: silicon oxynitride, silicon nitride, silicon nitride doped withcarbon, or silicon carbide. Processes for forming sidewall liners arewell-known in the art and generally include deposition and etchingprocess operations. In some embodiments, a plurality of liner pairs maybe used. For example, two pairs, three pairs, or four pairs of sidewallliners may be formed on opposing sides of the gate stack.

Gate metal layer 1307 may comprise at least one P-type work-functionmetal or N-type work-function metal, depending on whether the transistoris to be a p-type or an n-type transistor. Gate metal layer 1307 maycomprise a stack of two or more metal layers, where one or more metallayers are work-function metal layers and at least one metal layer is aconductive fill layer.

For an n-type transistor, metals that may be used for the gate metallayer 1307 include: aluminum carbide, tantalum carbide, zirconiumcarbide, and hafnium carbide. In some embodiments, metal for gate metallayer 1307 for n-type transistor include: aluminum, hafnium, zirconium,titanium, tantalum, and their alloys. An n-type metal layer will enablethe formation of an n-type gate metal layer 1307 with a work functionthat is between about 3.9 eV and about 4.2 eV. In some embodiments,metal of layer 1307 includes one of: TiN, TiSiN, TaN, Cu, Al, Au, W,TiSiN, or Co. In some embodiments, metal of layer 107 includes one ormore of: Ti, N, Si, Ta, Cu, Al, Au, W, or Co.

For a p-type transistor, metals that are used for gate metal layer 1307include, but are not limited to, ruthenium, palladium, platinum, cobalt,nickel, and conductive metal oxides. An example of conductive oxideincludes ruthenium oxide. A p-type metal layer will enable the formationof a p-type gate metal layer 1307 with a work function that is betweenabout 4.9 eV and about 5.2 eV.

Any suitable material can be used for drain and source contacts 1308 a/band via 1309 a/b. For example, one or more of Ti, N, Si, Ta, Cu, Al, Au,W, or Co can be used for drain and source contacts 1308 a/b and via 1309a/b. The gate electrodes 1307 may be connected to one another directlyor through vias and metal layers. Drivers (not shown) drive signals onnodes a, b, and c. The gates 1307 of MPinv and MNinv are coupledtogether. For example, gate electrodes 1307 may be connected to node Vsdirectly or through vias and metal layers 1316 and 1317, respectively.

FIGS. 14A-C illustrate a 2-input AND (or NAND) gate 1400 comprising twonon-linear capacitors, associated timing diagram 1420, and associatedcharges 1430, in accordance with some embodiments. In some embodiments,a 2-input AND gate (which can be transformed into a NAND gate) comprisesa first non-linear capacitor C1 n 1 and a second non-linear capacitor C1n 1. The first non-linear capacitor C1 n 1 receives a first input ‘a’(e.g., a digital input from a driver or another majority or minoritygate). The second non-linear capacitor C2 n 1 receives a first input ‘b’(e.g., a digital input from a driver or another majority or minoritygate). The two non-linear capacitors C1 n 1 and C2 n 1 connect to asumming node Vs where the AND function is performed. The result of theAND operation can be received by any majority or minority gate inaccordance with some embodiments. In some embodiments. the result of theAND function can be inverted or buffered. In some embodiments, node Vsis directly connected to another majority gate (e.g., a non-linearcapacitor of another gate). In some embodiments, inverters 101 and 1401are removed.

In one example, the summing node Vs is coupled to an input of aninverter 101 that generates an output “out” which provided a NANDfunction of the inputs ‘a’ and ‘b’. In some embodiments, the output“out” is inverted by inverter 1401 to generate an output “out_b” whichis an AND function of ‘a’ and ‘b’ (illustrated as AND_b(a,b)). The ANDgate of FIG. 14 mitigates the short circuit current leakage issue causedby non-rail-to-rail voltages on node Vs when linear input capacitors areused. When linear capacitors are used as input capacitors, when input‘a’ is a 1 and input ‘b’ is a zero, the voltage on Vs is half of input‘a’ and input ‘b’, which causes metastability. The non-linear inputcapacitors such as FE based capacitors or paraelectric based capacitors(or any other non-linear dielectric) result in near rail-to-rail voltageon node Vs which controls any crowbar current and/or leakage currentthrough subsequent driver circuitry like inverter 101. Here, themetastability problem is avoided by using non-linear input capacitors.Plot 1420 shows the timing diagram of AND gate 1400. Here, the lowvoltage on node Vs is low enough to trip inverter 101 to a high logiclevel output on node “out”, and the high voltage on node Vs is highenough to trip inverter 101 to a low logic level output on node “out”.As such, AND gate 1400 shows proper logic function and operation usingtwo non-linear input capacitors. Plot 1430 is similar to plot 1420, butalso shows the positive and negative charges on non-linear inputcapacitors C1 n 1 and C2 n 1.

FIG. 15 illustrates complex logic gate 1500 implemented using a 5-inputmajority gate, in accordance with some embodiments. In some embodiments,an AOI (and-or-invert) logic comprises a 5-input majority gate. The5-input majority gate includes non-linear capacitors C1 n 1, C2 n 1, C3n 1, C4 n 1, and C5 n 1 and driving circuitry 101 coupled as shown. Invarious embodiments, two of the non-linear capacitors receives the sameinput. Here, capacitors C3 n 1 and C4 n 1 receive input ‘c’. In variousembodiments, C5 n 1 is coupled to Vdd to produce an OR function at nodeVs, where the OR function is OR(AND(a,b),c). In some embodiments, otherlogic gates can be realized by changing Vdd to ground for capacitor C5 n1, and/or changing other inputs.

FIG. 16 illustrates a system-on-chip (SOC) 1600 that uses the majoritylogic gates having non-linear input capacitors, in accordance with someembodiments. SOC 1600 comprises memory 1601 having static random-accessmemory (SRAM) or FE based random access memory FE-RAM, or any othersuitable memory. The memory can be non-volatile (NV) or volatile memory.Memory 1601 may also comprise logic 1603 to control memory 1602. Forexample, write and read drivers are part of logic 1603. These driversand other logic are implemented using the majority or threshold gates ofvarious embodiments. The logic can comprise majority or threshold gatesand traditional logic (e.g., CMOS based NAND, NOR etc.).

SOC further comprises a memory I/O (input-output) interface 1604. Theinterface may be double-data rate (DDR) compliant interface or any othersuitable interface to communicate with a processor. Processor 1605 ofSOC 1600 can be a single core or multiple core processor. Processor 1605can be a general-purpose processor (CPU), a digital signal processor(DSP), or an Application Specific Integrated Circuit (ASIC) processor.In some embodiments, processor 1605 is an artificial intelligence (AI)processor (e.g., a dedicated AI processor, a graphics processorconfigured as an AI processor). In various embodiments, processor 1605is a processor circuitry which is to execute one or more instructions.

AI is a broad area of hardware and software computations where data isanalyzed, classified, and then a decision is made regarding the data.For example, a model describing classification of data for a certainproperty or properties is trained over time with large amounts of data.The process of training a model requires large amounts of data andprocessing power to analyze the data. When a model is trained, weightsor weight factors are modified based on outputs of the model. Onceweights for a model are computed to a high confidence level (e.g., 95%or more) by repeatedly analyzing data and modifying weights to get theexpected results, the model is deemed “trained.” This trained model withfixed weights is then used to make decisions about new data. Training amodel and then applying the trained model for new data is hardwareintensive activity. In some embodiments, AI processor 405 has reducedlatency of computing the training model and using the training model,which reduces the power consumption of such AI processor systems.

Processor 1605 may be coupled to a number of other chip-lets that can beon the same die as SOC 1600 or on separate dies. These chip-lets includeconnectivity circuitry 1606, I/O controller 1607, power management 1608,and display system 1609, and peripheral connectivity 1610.

Connectivity 1606 represents hardware devices and software componentsfor communicating with other devices. Connectivity 1606 may supportvarious connectivity circuitries and standards. For example,connectivity 1606 may support GSM (global system for mobilecommunications) or variations or derivatives, CDMA (code divisionmultiple access) or variations or derivatives, TDM (time divisionmultiplexing) or variations or derivatives, 3rd Generation PartnershipProject (3GPP) Universal Mobile Telecommunications Systems (UMTS) systemor variations or derivatives, 3GPP Long-Term Evolution (LTE) system orvariations or derivatives, 3GPP LTE-Advanced (LTE-A) system orvariations or derivatives, Fifth Generation (5G) wireless system orvariations or derivatives, 5G mobile networks system or variations orderivatives, 5G New Radio (NR) system or variations or derivatives, orother cellular service standards. In some embodiments, connectivity 1606may support non-cellular standards such as WiFi.

I/O controller 1607 represents hardware devices and software componentsrelated to interaction with a user. I/O controller 1607 is operable tomanage hardware that is part of an audio subsystem and/or displaysubsystem. For example, input through a microphone or other audio devicecan provide input or commands for one or more applications or functionsof SOC 1600. In some embodiments, I/O controller 1607 illustrates aconnection point for additional devices that connect to SOC 1600 throughwhich a user might interact with the system. For example, devices thatcan be attached to the SOC 1600 might include microphone devices,speaker or stereo systems, video systems or other display devices,keyboard or keypad devices, or other I/O devices for use with specificapplications such as card readers or other devices.

Power management 1608 represents hardware or software that perform powermanagement operations, e.g., based at least in part on receivingmeasurements from power measurement circuitries, temperature measurementcircuitries, charge level of battery, and/or any other appropriateinformation that may be used for power management. By using majority andthreshold gates of various embodiments, non-volatility is achieved atthe output of these logic. Power management 1608 may accordingly putsuch logic into low power state without the worry of losing data. Powermanagement may select a power state according to Advanced Configurationand Power Interface (ACPI) specification for one or all components ofSOC 1600.

Display system 1609 represents hardware (e.g., display devices) andsoftware (e.g., drivers) components that provide a visual and/or tactiledisplay for a user to interact with the processor 1605. In someembodiments, display system 1609 includes a touch screen (or touch pad)device that provides both output and input to a user. Display system1609 may include a display interface, which includes the particularscreen or hardware device used to provide a display to a user. In someembodiments, the display interface includes logic separate fromprocessor 1605 to perform at least some processing related to thedisplay.

Peripheral connectivity 1610 may represent hardware devices and/orsoftware devices for connecting to peripheral devices such as printers,chargers, cameras, etc. Peripheral connectivity 1610 may supportcommunication protocols, e.g., PCIe (Peripheral Component InterconnectExpress), USB (Universal Serial Bus), Thunderbolt, High DefinitionMultimedia Interface (HDMI), Firewire, etc.

Reference in the specification to “an embodiment,” “one embodiment,”“some embodiments,” or “other embodiments” means that a particularfeature, structure, or characteristic described in connection with theembodiments is included in at least some embodiments, but notnecessarily all embodiments. The various appearances of “an embodiment,”“one embodiment,” or “some embodiments” are not necessarily allreferring to the same embodiments. If the specification states acomponent, feature, structure, or characteristic “may,” “might,” or“could” be included, that particular component, feature, structure, orcharacteristic is not required to be included. If the specification orclaim refers to “a” or “an” element, that does not mean there is onlyone of the elements. If the specification or claims refer to “anadditional” element, that does not preclude there being more than one ofthe additional elements.

Furthermore, the particular features, structures, functions, orcharacteristics may be combined in any suitable manner in one or moreembodiments. For example, a first embodiment may be combined with asecond embodiment anywhere the particular features, structures,functions, or characteristics associated with the two embodiments arenot mutually exclusive.

While the disclosure has been described in conjunction with specificembodiments thereof, many alternatives, modifications and variations ofsuch embodiments will be apparent to those of ordinary skill in the artin light of the foregoing description. The embodiments of the disclosureare intended to embrace all such alternatives, modifications, andvariations as to fall within the broad scope of the appended claims.

In addition, well-known power/ground connections to integrated circuit(IC) chips and other components may or may not be shown within thepresented figures, for simplicity of illustration and discussion, and soas not to obscure the disclosure. Further, arrangements may be shown inblock diagram form in order to avoid obscuring the disclosure, and alsoin view of the fact that specifics with respect to implementation ofsuch block diagram arrangements are highly dependent upon the platformwithin which the present disclosure is to be implemented (i.e., suchspecifics should be well within purview of one skilled in the art).Where specific details (e.g., circuits) are set forth in order todescribe example embodiments of the disclosure, it should be apparent toone skilled in the art that the disclosure can be practiced without, orwith variation of, these specific details. The description is thus to beregarded as illustrative instead of limiting.

Following examples are provided that illustrate the various embodiments.The examples can be combined with other examples. As such, variousembodiments can be combined with other embodiments without changing thescope of the invention. For example, example 7 can be combined withexample 3 or 2, or both.

Example 1: An apparatus comprising: a first capacitor to receive a firstinput, the first capacitor coupled to a node; a second capacitor toreceive a second input, the second capacitor coupled to the node; athird capacitor to receive a third input, wherein the third capacitor iscoupled to the node, wherein the first capacitor, the second capacitor,and the third capacitor include non-linear polar material; and a drivercircuitry having a capacitive input coupled to the node, and an outputwhich is to provide a majority or minority logic function of the firstinput, the second input, and the third input.

Example 2: The apparatus of example 1, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 3: The apparatus of example 2, wherein the ferroelectricmaterial includes one of: bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 4: The apparatus of example 2, wherein the paraelectric materialincludes one of: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and y is0.95), HfZrO2, Hf—Si—O, La-substituted PbTiO3, or PMN-PT based relaxorferroelectrics.

Example 5: The apparatus of example 2, wherein the paraelectric materialincludes one of: Sr, Ti, Ba, Hf, Zr, Si, La, or Pb.

Example 6: The apparatus of example 1, wherein the first input, thesecond input, and the third input are digital signals, wherein the nodehas a voltage which is either at ground level or a supply level.

Example 7: The apparatus of example 1 comprising a fourth capacitorcoupled to the node and a ground terminal, wherein the fourth capacitoris a linear capacitor or non-linear capacitor.

Example 8: The apparatus of example 1, wherein the driver circuitrycomprises one of: an inverter; a buffer; a CMOS circuitry; a majoritygate; a minority gate; a linear capacitor; or a non-linear capacitor.

Example 9: The apparatus of example 1, wherein when the third input isat ground level, a voltage on the node is an AND logic function of thefirst input and the second input.

Example 10: The apparatus of example 1, wherein when the third input isat supply level, a voltage on the node is an OR logic function of thefirst input and the second input.

Example 11: An apparatus comprising: first, second, and third drivers togenerate first, second, and third digital signals, respectively; first,second, and third non-linear capacitors to receive the first, second,and third digital signals, respectively; and a node to sum charges ofthe first, second, and third non-linear capacitors; and a CMOS logic todrive a voltage on the node.

Example 12: The apparatus of example 11, wherein the first, second, andthird non-linear capacitors comprise non-linear polar material whichincludes one of: ferroelectric material, para-electric material, ornon-linear dielectric.

Example 13: The apparatus of example 12, wherein the ferroelectricmaterial includes one of: bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 14: The apparatus of example 11, wherein when the third digitalsignal is at ground level, a voltage on the node is an AND logicfunction of the first digital signal and the second digital signal.

Example 15: The apparatus of example 11, wherein when the third digitalsignal is at supply level, a voltage on the node is an OR logic functionof the first digital signal and the second digital signal.

Example 16: The apparatus of example 11, wherein the voltage on the nodeis a rail-to-rail voltage.

Example 17: A system comprising: a processor circuitry to execute one ormore instructions; a communication interface communicatively coupled tothe processor circuitry; and a memory coupled to the processorcircuitry, wherein the processor circuitry comprises a majority gatelogic which includes: a first capacitor to receive a first input, thefirst capacitor coupled to a node; a second capacitor to receive asecond input, the second capacitor coupled to the node; a thirdcapacitor to receive a third input, wherein the third capacitor iscoupled to the node, wherein the first capacitor, the second capacitor,and the third capacitor include non-linear polar material; and a drivercircuitry having a capacitive input coupled to the node, and an outputwhich is to provide a majority or minority logic function of the firstinput, the second input, and the third input.

Example 18: The system of example 17, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 19: The system of example 18, wherein the ferroelectric materialincludes one of: bismuth ferrite (BFO), BFO with a doping materialwherein the doping material is one of Lanthanum, or elements fromlanthanide series of periodic table; lead zirconium titanate (PZT), orPZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 20: The apparatus of example 18, wherein the paraelectricmaterial includes one of: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and yis 0.95), HfZrO2, Hf—Si—O, La-substituted PbTiO3, or PMN-PT basedrelaxor ferroelectrics.

Example 21: A method comprising: forming a first capacitor to receive afirst input, the first capacitor coupled to a node; forming a secondcapacitor to receive a second input, the second capacitor coupled to thenode; forming a third capacitor to receive a third input, wherein thethird capacitor is coupled to the node, wherein the first capacitor, thesecond capacitor, and the third capacitor include non-linear polarmaterial; and forming a driver circuitry having a capacitive inputcoupled to the node, and an output which is provide a majority orminority logic function of the first input, the second input, and thethird input.

Example 22: The method of example 21, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 23: The method of example 22, wherein the ferroelectric materialincludes one of: bismuth ferrite (BFO), BFO with a doping materialwherein the doping material is one of Lanthanum, or elements fromlanthanide series of periodic table; lead zirconium titanate (PZT), orPZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 24: The method of example 21, wherein the node has a voltagewhich is either at ground level or a supply level.

Example 25: The method of example 21, wherein the first input, thesecond input, and the third input are digital signals.

Example 26: The method of example 21 comprising forming a fourthcapacitor coupled to the node and a ground terminal, wherein the fourthcapacitor is a linear capacitor.

Example 27: The method of example 21, wherein forming the drivercircuitry comprises forming an inverter, forming a CMOS circuitry,forming a buffer, forming a linear capacitor, forming a non-linearcapacitor, forming a majority gate, or a forming a minority gate.

Example 28: The method of example 21, wherein when the third input is atground level, a voltage on the node is an AND logic function of thefirst input and the second input.

Example 29: The method of example 21, wherein when the third input is atsupply level, a voltage on the node is an OR logic function of the firstinput and the second input.

Example 1b. An apparatus comprising: a NAND logic gate comprising firstthree non-linear capacitors and an inverter; an OR logic gate comprisingsecond three non-linear capacitors; and an AND logic gate comprisingthird three non-linear capacitors, wherein the AND logic gate is toperform a majority logic function on an output of the NAND logic gateand an output of the OR logic gate.

Example 2b. The apparatus of example 1b, wherein the NAND logic gatecomprises: a first capacitor to receive a first input, the firstcapacitor coupled to a first node; a second capacitor to receive asecond input, the second capacitor coupled to the first node; a thirdcapacitor to receive a third input, wherein the first capacitor, thethird capacitor coupled to the first node; and an inverter having acapacitive input coupled to the first node, and an output which isprovide a minority logic function of the first input, the second input,and the third input, wherein the first three non-linear capacitorsinclude the first capacitor, the second capacitor, and the thirdcapacitor, wherein the output of the inverter is the output of the NANDlogic gate, wherein the third input is coupled to a ground node.

Example 3b: The apparatus of example 2b, wherein the OR logic gateincludes: a fourth capacitor to receive the first input, the fourthcapacitor coupled to a second node; a fifth capacitor to receive thesecond input, the fifth capacitor coupled to the second node; and asixth capacitor to receive a fourth input, wherein the sixth capacitoris coupled to the second node, wherein the second three non-linearcapacitors include the fourth capacitor, the fifth capacitor, and thesixth capacitor, wherein the second node provides the output of the ORlogic gate, wherein the fourth input is coupled to a supply node.

Example 4b: The apparatus of example 3b, wherein the AND logic gateincludes: a seventh capacitor to receive the output of the NAND logicgate, the seventh capacitor coupled to a third node; an eighth capacitorto receive the output of the OR logic gate, the eighth capacitor coupledto the third node; and a ninth capacitor to receive a fifth input,wherein the ninth capacitor is coupled to the third node, wherein thethird three non-linear capacitors include the seventh capacitor, theeighth capacitor, and the ninth capacitor, wherein the third nodeprovides an XOR function of the first input and the second input,wherein the fifth input is coupled to the ground node.

Example 5b: The apparatus of example 1b, wherein the first threenon-linear capacitors, second three non-linear capacitors, and thirdthree non-linear capacitors comprise non-linear polar material whichincludes one of: ferroelectric material, para-electric material, ornon-linear dielectric.

Example 6b: The apparatus of example 5b, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,or Nb; relaxor ferroelectric which includes one of lead magnesiumniobate (PMN), lead magnesium niobate-lead titanate (PMN-PT), leadlanthanum zirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1-x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 7b: The apparatus of example 5b, wherein the paraelectricmaterial includes one of: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and yis 0.95), HfZrO2, Hf—Si—O, La-substituted PbTiO3, or PMN-PT basedrelaxor ferroelectrics.

Example 8b: The apparatus of example 4b, wherein a first voltage on thefirst node is a rail-to-rail voltage, which is either at a ground levelor a supply level, wherein a second voltage on the second node is arail-to-rail voltage, which is either at a ground level or a supplylevel, wherein a third voltage on the third node is a rail-to-railvoltage, which is either at a ground level or a supply level.

Example 9b: The apparatus of example 4b, wherein the first input and thesecond input are digital signals.

Example 10b: A method comprising: forming a NAND logic gate comprisingfirst three non-linear capacitors and an inverter; forming an OR logicgate comprising second three non-linear capacitors; and forming an ANDlogic gate comprising third three non-linear capacitors, wherein the ANDlogic gate is to perform a majority logic function on an output of theNAND logic gate and an output of the OR logic gate.

Example 11b: The method of example 10b, wherein forming the NAND logicgate comprises: forming a first capacitor to receive a first input, thefirst capacitor coupled to a first node; forming a second capacitor toreceive a second input, the second capacitor coupled to the first node;forming a third capacitor to receive a third input, wherein the firstcapacitor, the third capacitor coupled to the first node; and forming aninverter having a capacitive input coupled to the first node, and anoutput which is provide a minority logic function of the first input,the second input, and the third input, wherein the first threenon-linear capacitors include the first capacitor, the second capacitor,and the third capacitor, wherein the output of the inverter is theoutput of the NAND logic gate.

Example 12b: The method of example 11b, wherein forming the OR logicgate includes: forming a fourth capacitor to receive the first input,the fourth capacitor coupled to a second node; forming a fifth capacitorto receive the second input, the fifth capacitor coupled to the secondnode; and forming a sixth capacitor to receive a fourth input, whereinthe sixth capacitor is coupled to the second node, wherein the secondthree non-linear capacitors include the fourth capacitor, the fifthcapacitor, and the sixth capacitor, wherein the second node provides theoutput of the OR logic gate.

Example 13b: The method of example 12b, wherein forming the AND logicgate includes: forming a seventh capacitor to receive the output of theNAND logic gate, the seventh capacitor coupled to a third node; formingan eighth capacitor to receive the output of the OR logic gate, theeighth capacitor coupled to the third node; and forming a ninthcapacitor to receive a fifth input, wherein the ninth capacitor iscoupled to the third node, wherein the third three non-linear capacitorsinclude the seventh capacitor, the eighth capacitor, and the ninthcapacitor, wherein the third node provides an XOR function of the firstinput and the second input.

Example 14b: The method of example 13b comprising: coupling the thirdinput to a ground node; coupling the fourth input to a supply node; andcoupling the fifth input to the ground node.

Example 15b: The method of example 10b, wherein the first threenon-linear capacitors, second three non-linear capacitors, and thirdthree non-linear capacitors comprise non-linear polar material whichincludes one of: ferroelectric material, para-electric material, ornon-linear dielectric.

Example 16b: The method of example 15b, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,or Nb; relaxor ferroelectric which includes one of lead magnesiumniobate (PMN), lead magnesium niobate-lead titanate (PMN-PT), leadlanthanum zirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1-x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 17b: The method of example 13b comprising providing the firstinput and the second input as digital signals.

Example 18b: A system comprising: a processor circuitry to execute oneor more instructions; a communication interface communicatively coupledto the processor circuitry; and a memory coupled to the processorcircuitry, wherein the processor circuitry comprises a XOR logic whichincludes: a NAND logic gate comprising first three non-linear capacitorsand an inverter; an OR logic gate comprising second three non-linearcapacitors; and an AND logic gate comprising third three non-linearcapacitors, wherein the AND logic gate is to perform a majority logicfunction on an output of the NAND logic gate and an output of the ORlogic gate.

Example 19b: The system of example 18b, wherein the NAND logic gatecomprises: a first capacitor to receive a first input, the firstcapacitor coupled to a first node; a second capacitor to receive asecond input, the second capacitor coupled to the first node; a thirdcapacitor to receive a third input, wherein the first capacitor, thethird capacitor coupled to the first node; and an inverter having acapacitive input coupled to the first node, and an output which isprovide a minority logic function of the first input, the second input,and the third input, wherein the first three non-linear capacitorsinclude the first capacitor, the second capacitor, and the thirdcapacitor, wherein the output of the inverter is the output of the NANDlogic gate.

Example 20b: The system of example 19b, wherein the OR logic gateincludes: a fourth capacitor to receive the first input, the fourthcapacitor coupled to a second node; a fifth capacitor to receive thesecond input, the fifth capacitor coupled to the second node; and asixth capacitor to receive a fourth input, wherein the sixth capacitoris coupled to the second node, wherein the second three non-linearcapacitors include the fourth capacitor, the fifth capacitor, and thesixth capacitor, wherein the second node provides the output of the ORlogic gate; wherein the AND logic gate includes: a seventh capacitor toreceive the output of the NAND logic gate, the seventh capacitor coupledto a third node; an eighth capacitor to receive the output of the ORlogic gate, the eighth capacitor coupled to the third node; and a ninthcapacitor to receive a fifth input, wherein the ninth capacitor iscoupled to the third node, wherein the third three non-linear capacitorsinclude the seventh capacitor, the eighth capacitor, and the ninthcapacitor, wherein the third node provides an XOR function of the firstinput and the second input.

Example 1c: An apparatus comprising: a AND logic gate comprising firstthree non-linear capacitors and an inverter; and an NOR logic gatecomprising second three non-linear capacitors, wherein an output of theAND logic gate is provided as input to the NOR logic gate, wherein anoutput of the NOR logic gate is an AND-OR-INVERT (AOI) logic function.

Example 2c: The apparatus of example 1c, wherein the AND logic gatecomprises: a first capacitor to receive a first input, the firstcapacitor coupled to a first node; a second capacitor to receive asecond input, the second capacitor coupled to the first node; and athird capacitor to receive a third input, wherein the first capacitor,the third capacitor are coupled to the first node; wherein the firstthree non-linear capacitors include the first capacitor, the secondcapacitor, and the third capacitor.

Example 3c: The apparatus of example 2c, wherein the NOR logic gateincludes: a fourth capacitor to receive the fourth input, the fourthcapacitor coupled to a second node; a fifth capacitor to receive theoutput of the AND gate, the fifth capacitor coupled to the second node;a sixth capacitor to receive a fifth input, wherein the sixth capacitoris coupled to the second node, wherein the second three non-linearcapacitors include the fourth capacitor, the fifth capacitor, and thesixth capacitor; and an inverter having an input coupled to the secondnode, wherein an output of the inverter is the AOI logic function.

Example 4c: The apparatus of example 3c, wherein the third input iscoupled to a ground node, and wherein the fifth input is coupled to asupply node.

Example 5c: The apparatus of example 1c, wherein the first threenon-linear capacitors and the second three non-linear capacitorscomprise non-linear polar material which includes one of: ferroelectricmaterial, para-electric material, or non-linear dielectric.

Example 6c: The apparatus of example 5c, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of Laor Nb; relaxor ferroelectric which includes one of lead magnesiumniobate (PMN), lead magnesium niobate-lead titanate (PMN-PT), leadlanthanum zirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 7c: The apparatus of example 3c, wherein a first voltage on thefirst node is a rail-to-rail voltage, which is either at a ground levelor a supply level, wherein a second voltage on the second node is arail-to-rail voltage, which is either at a ground level or a supplylevel.

Example 8c: The apparatus of example 3c, wherein the first input, thesecond input, and the fourth inputs are digital signals.

Example 9c: A method comprising: forming a AND logic gate comprisingfirst three non-linear capacitors and an inverter; and forming an NORlogic gate comprising second three non-linear capacitors, wherein anoutput of the AND logic gate is provided as input to the NOR logic gate,wherein an output of the NOR logic gate is an AND-OR-INVERT (AOI) logicfunction.

Example 10c: The method of example 9c, wherein forming the AND logicgate comprises: forming a first capacitor to receive a first input, thefirst capacitor coupled to a first node; forming a second capacitor toreceive a second input, the second capacitor coupled to the first node;and forming a third capacitor to receive a third input, wherein thefirst capacitor, the third capacitor are coupled to the first node;wherein the first three non-linear capacitors include the firstcapacitor, the second capacitor, and the third capacitor.

Example 11c: The method of example 10c, wherein forming the NOR logicgate includes: forming a fourth capacitor to receive the fourth input,the fourth capacitor coupled to a second node; forming a fifth capacitorto receive the output of the AND gate, the fifth capacitor coupled tothe second node; forming a sixth capacitor to receive a fifth input,wherein the sixth capacitor is coupled to the second node, wherein thesecond three non-linear capacitors include the fourth capacitor, thefifth capacitor, and the sixth capacitor; and forming an inverter havingan input coupled to the second node, wherein an output of the inverteris the AOI logic function.

Example 12c: The method of example 11c comprising: coupling the thirdinput to a ground node, and coupling the fifth input to a supply node.

Example 13c: The method of example 9c, wherein the first threenon-linear capacitors and the second three non-linear capacitorscomprise non-linear polar material which includes one of: ferroelectricmaterial, para-electric material, or non-linear dielectric.

Example 14c: The method of example 13c, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of Laor Nb; relaxor ferroelectric which includes one of lead magnesiumniobate (PMN), lead magnesium niobate-lead titanate (PMN-PT), leadlanthanum zirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 15c: The method of example 11c, wherein a first voltage on thefirst node is a rail-to-rail voltage, which is either at a ground levelor a supply level, wherein a second voltage on the second node is arail-to-rail voltage, which is either at a ground level or a supplylevel.

Example 16c: The method of example 11c, wherein the first input, thesecond input, and the fourth inputs are digital signals.

Example 17c: A system comprising: a processor circuitry to execute oneor more instructions; a communication interface communicatively coupledto the processor circuitry; and a memory coupled to the processorcircuitry, wherein the processor circuitry comprises an AND-OR-inverterlogic which includes: a AND logic gate comprising first three non-linearcapacitors and an inverter; and an NOR logic gate comprising secondthree non-linear capacitors, wherein an output of the AND logic gate isprovided as input to the NOR logic gate, wherein an output of the NORlogic gate is an AND-OR-INVERT (AOI) logic function.

Example 18c: The system of example 17c, wherein the AND logic gatecomprises: a first capacitor to receive a first input, the firstcapacitor coupled to a first node; a second capacitor to receive asecond input, the second capacitor coupled to the first node; and athird capacitor to receive a third input, wherein the first capacitor,the third capacitor are coupled to the first node; wherein the firstthree non-linear capacitors include the first capacitor, the secondcapacitor, and the third capacitor.

Example 19c: The system of example 18c, wherein the NOR logic gateincludes: a fourth capacitor to receive the fourth input, the fourthcapacitor coupled to a second node; a fifth capacitor to receive theoutput of the AND gate, the fifth capacitor coupled to the second node;a sixth capacitor to receive a fifth input, wherein the sixth capacitoris coupled to the second node, wherein the second three non-linearcapacitors include the fourth capacitor, the fifth capacitor, and thesixth capacitor; and an inverter having an input coupled to the secondnode, wherein an output of the inverter is the AOI logic function.

Example 20c: The system of example 19c, wherein the third input iscoupled to a ground node, and wherein the fifth input is coupled to asupply node.

Example 1d: An apparatus comprising: a first capacitor to receive afirst input, the first capacitor coupled to a node; a second capacitorto receive a second input, the second capacitor coupled to the node,wherein the first capacitor and the second capacitor include non-linearpolar material; and a logic gate coupled to the node.

Example 2d: The apparatus of example 1d, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 3d: The apparatus of example 2d, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 4d: The apparatus of example 2d, wherein the paraelectricmaterial includes one of: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and yis 0.95), HfZrO2, Hf—Si—O, La-substituted PbTiO3, or PMN-PT basedrelaxor ferroelectrics.

Example 5d: The apparatus of example 2d, wherein the paraelectricmaterial includes one of: Sr, Ti, Ba, Hf, Zr, Pb, or La.

Example 6d: The apparatus of example 1d, wherein the first input and thesecond input are digital signals.

Example 7d: The apparatus of example 1d, wherein the logic gate is amajority or minority gate having non-linear input capacitors.

Example 8d: The apparatus of example 1d, wherein the logic gate is aCMOS gate.

Example 9d: The apparatus of example 1d, wherein the logic gate is aninverter, wherein an output of the inverter is a NAND function of thefirst input and the second input.

Example 10d: A method comprising: forming a first capacitor to receive afirst input, the first capacitor coupled to a node; forming a secondcapacitor to receive a second input, the second capacitor coupled to thenode, wherein the first capacitor and the second capacitor includenon-linear polar material; and coupling a logic gate to the node.

Example 11d: The method of example 10d, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 12d: The method of example 11d, wherein the ferroelectricmaterial includes one of: Bismuth ferrite (BFO), BFO with a dopingmaterial wherein the doping material is one of Lanthanum, or elementsfrom lanthanide series of periodic table; Lead zirconium titanate (PZT),or PZT with a doping material, wherein the doping material is one of La,Nb; relaxor ferroelectric which includes one of lead magnesium niobate(PMN), lead magnesium niobate-lead titanate (PMN-PT), lead lanthanumzirconate titanate (PLZT), lead scandium niobate (PSN), BariumTitanium-Bismuth Zinc Niobium Tantalum (BT-BZNT), or BariumTitanium-Barium Strontium Titanium (BT-BST); perovskite includes one of:BaTiO3, PbTiO3, KNbO3, or NaTaO3; hexagonal ferroelectric includes oneof: YMnO3, or LuFeO3; hexagonal ferroelectrics of a type h-RMnO3, whereR is a rare earth element which includes one of: cerium (Ce), dysprosium(Dy), erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho),lanthanum (La), lutetium (Lu), neodymium (Nd), praseodymium (Pr),promethium (Pm), samarium (Sm), scandium (Sc), terbium (Tb), thulium(Tm), ytterbium (Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr),Aluminum (Al), Silicon (Si), their oxides or their alloyed oxides;Hafnium oxides as Hf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, er, Gd,Ge, La, Sc, Si, Sr, Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)Nor Al(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca,Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or improper ferroelectric includes one of: [PTO/STO]nor [LAO/STO]n, where ‘n’ is between 1 to 100.

Example 13d: The method of example 11d, wherein the paraelectricmaterial includes one of: SrTiO3, Ba(x)Sr(y)TiO3 (where x is −0.5, and yis 0.95), HfZrO2, Hf—Si—O, La-substituted PbTiO3, or PMN-PT basedrelaxor ferroelectrics.

Example 14d: The method of example 11d, wherein the paraelectricmaterial includes one of: Sr, Ti, Ba, Hf, Zr, Pb, or La.

Example 15d: The method of example 10d, wherein the first input and thesecond input are digital signals.

Example 16d: The method of example 10d, wherein the logic gate is: amajority or minority gate having non-linear input capacitors; a CMOSgate; or an inverter, wherein an output of the inverter is a NANDfunction of the first input and the second input.

Example 17d: A system comprising: a processor circuitry to execute oneor more instructions; a communication interface communicatively coupledto the processor circuitry; and a memory coupled to the processorcircuitry, wherein the processor circuitry comprises a NAND gate whichincludes: a first capacitor to receive a first input, the firstcapacitor coupled to a node; a second capacitor to receive a secondinput, the second capacitor coupled to the node, wherein the firstcapacitor and the second capacitor include non-linear polar material;and a logic gate coupled to the node.

Example 18d: The system of example 17d, wherein the non-linear polarmaterial includes one of: ferroelectric material, para-electricmaterial, or non-linear dielectric.

Example 19d: The system of example 17d, wherein the logic gate is: amajority or minority gate having non-linear input capacitors; a CMOSgate; or an inverter, wherein an output of the inverter is a NANDfunction of the first input and the second input.

Example 20d: The system of example 17d, wherein the first input and thesecond input are digital signals.

An abstract is provided that will allow the reader to ascertain thenature and gist of the technical disclosure. The abstract is submittedwith the understanding that it will not be used to limit the scope ormeaning of the claims. The following claims are hereby incorporated intothe detailed description, with each claim standing on its own as aseparate embodiment.

We claim:
 1. An apparatus comprising: a AND logic gate comprising firstthree non-linear capacitors and an inverter; and an NOR logic gatecomprising second three non-linear capacitors, wherein an output of theAND logic gate is provided as input to the NOR logic gate, and whereinan output of the NOR logic gate is an AND-OR-INVERT (AOI) logicfunction.
 2. The apparatus of claim 1, wherein the AND logic gatecomprises: a first capacitor to receive a first input, the firstcapacitor coupled to a first node; a second capacitor to receive asecond input, the second capacitor coupled to the first node; and athird capacitor to receive a third input, wherein the first capacitorand the third capacitor are coupled to the first node; wherein the firstthree non-linear capacitors include the first capacitor, the secondcapacitor, and the third capacitor.
 3. The apparatus of claim 2, whereinthe NOR logic gate includes: a fourth capacitor to receive a fourthinput, the fourth capacitor coupled to a second node; a fifth capacitorto receive the output of the AND logic gate, the fifth capacitor coupledto the second node; a sixth capacitor to receive a fifth input, whereinthe sixth capacitor is coupled to the second node, and wherein thesecond three non-linear capacitors include the fourth capacitor, thefifth capacitor, and the sixth capacitor; and an inverter having aninput coupled to the second node, wherein an output of the inverter isthe AOI logic function.
 4. The apparatus of claim 3, wherein the thirdinput is coupled to a ground node, and wherein the fifth input iscoupled to a supply node.
 5. The apparatus of claim 3, wherein a firstvoltage on the first node is a rail-to-rail voltage, which is either ata ground level or a supply level, wherein a second voltage on the secondnode is a rail-to-rail voltage, which is either at a ground level or asupply level.
 6. The apparatus of claim 3, wherein the first input, thesecond input, and the fourth input are digital signals.
 7. The apparatusof claim 1, wherein the first three non-linear capacitors and the secondthree non-linear capacitors comprise non-linear polar material whichincludes one of: a ferroelectric material, a para-electric material, ora non-linear dielectric.
 8. The apparatus of claim 7, wherein theferroelectric material includes one of: Bismuth ferrite (BFO), BFO witha doping material wherein the doping material is one of Lanthanum, orelements from lanthanide series of periodic table; Lead zirconiumtitanate (PZT), or PZT with a doping material, wherein the dopingmaterial is one of La or Nb; a relaxor ferroelectric which includes oneof lead magnesium niobate (PMN), lead magnesium niobate-lead titanate(PMN-PT), lead lanthanum zirconate titanate (PLZT), lead scandiumniobate (PSN), Barium Titanium-Bismuth Zinc Niobium Tantalum (BT-BZNT),or Barium Titanium-Barium Strontium Titanium (BT-BST); a perovskitewhich includes one of: BaTiO3, PbTiO3, KNbO3, or NaTaO3; an hexagonalferroelectric which includes one of: YMnO3 or LuFeO3; hexagonalferroelectrics of a type h-RMnO3, where R is a rare earth element whichincludes one of: cerium (Ce), dysprosium (Dy), erbium (Er), europium(Eu), gadolinium (Gd), holmium (Ho), lanthanum (La), lutetium (Lu),neodymium (Nd), praseodymium (Pr), promethium (Pm), samarium (Sm),scandium (Sc), terbium (Tb), thulium (Tm), ytterbium (Yb), or yttrium(Y); Hafnium (Hf), Zirconium (Zr), Aluminum (Al), Silicon (Si), theiroxides or their alloyed oxides; Hafnium oxides as Hf1−x Ex Oy, where Ecan be Al, Ca, Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y;Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)N or Al(1−x−y)Mg(x)Nb(y)N, ydoped HfO2, where x includes one of: Al, Ca, Ce, Dy, Er, Gd, Ge, La, Sc,Si, Sr, Sn, or Y, wherein ‘x’ is a fraction; Niobate type compoundsLiNbO3, LiTaO3, Lithium iron Tantalum Oxy Fluoride, Barium StrontiumNiobate, Sodium Barium Niobate, or Potassium strontium niobate; or animproper ferroelectric which includes one of: [PTO/STO]n or [LAO/STO]n,where ‘n’ is between 1 to
 100. 9. A method comprising: forming a ANDlogic gate comprising first three non-linear capacitors and an inverter;and forming an NOR logic gate comprising second three non-linearcapacitors, wherein an output of the AND logic gate is provided as inputto the NOR logic gate, and wherein an output of the NOR logic gate is anAND-OR-INVERT (AOI) logic function.
 10. The method of claim 9, whereinforming the AND logic gate comprises: forming a first capacitor toreceive a first input, the first capacitor coupled to a first node;forming a second capacitor to receive a second input, the secondcapacitor coupled to the first node; and forming a third capacitor toreceive a third input, wherein the first capacitor and the thirdcapacitor are coupled to the first node; wherein the first threenon-linear capacitors include the first capacitor, the second capacitor,and the third capacitor.
 11. The method of claim 10, wherein forming theNOR logic gate includes: forming a fourth capacitor to receive a fourthinput, the fourth capacitor coupled to a second node; forming a fifthcapacitor to receive the output of the AND logic gate, the fifthcapacitor coupled to the second node; forming a sixth capacitor toreceive a fifth input, wherein the sixth capacitor is coupled to thesecond node, wherein the second three non-linear capacitors include thefourth capacitor, the fifth capacitor, and the sixth capacitor; andforming an inverter having an input coupled to the second node, whereinan output of the inverter is the AOI logic function.
 12. The method ofclaim 11 comprising: coupling the third input to a ground node, andcoupling the fifth input to a supply node.
 13. The method of claim 11,wherein a first voltage on the first node is a rail-to-rail voltage,which is either at a ground level or a supply level, wherein a secondvoltage on the second node is a rail-to-rail voltage, which is either ata ground level or a supply level.
 14. The method of claim 11, whereinthe first input, the second input, and the fourth input are digitalsignals.
 15. The method of claim 9, wherein the first three non-linearcapacitors and the second three non-linear capacitors comprisenon-linear polar material which includes one of: a ferroelectricmaterial, a para-electric material, or a non-linear dielectric.
 16. Themethod of claim 15, wherein the ferroelectric material includes one of:Bismuth ferrite (BFO), BFO with a doping material wherein the dopingmaterial is one of Lanthanum, or elements from lanthanide series ofperiodic table; Lead zirconium titanate (PZT), or PZT with a dopingmaterial, wherein the doping material is one of La or Nb; a relaxorferroelectric which includes one of lead magnesium niobate (PMN), leadmagnesium niobate-lead titanate (PMN-PT), lead lanthanum zirconatetitanate (PLZT), lead scandium niobate (PSN), Barium Titanium-BismuthZinc Niobium Tantalum (BT-BZNT), or Barium Titanium-Barium StrontiumTitanium (BT-BST); a perovskite includes one of: BaTiO3, PbTiO3, KNbO3,or NaTaO3; an hexagonal ferroelectric which includes one of: YMnO3, orLuFeO3; hexagonal ferroelectrics of a type h-RMnO3, where R is a rareearth element which includes one of: cerium (Ce), dysprosium (Dy),erbium (Er), europium (Eu), gadolinium (Gd), holmium (Ho), lanthanum(La), lutetium (Lu), neodymium (Nd), praseodymium (Pr), promethium (Pm),samarium (Sm), scandium (Sc), terbium (Tb), thulium (Tm), ytterbium(Yb), or yttrium (Y); Hafnium (Hf), Zirconium (Zr), Aluminum (Al),Silicon (Si), their oxides or their alloyed oxides; Hafnium oxides asHf1−x Ex Oy, where E can be Al, Ca, Ce, Dy, Er, Gd, Ge, La, Sc, Si, Sr,Sn, or Y; Al(1−x)Sc(x)N, Ga(1−x)Sc(x)N, Al(1−x)Y(x)N orAl(1−x−y)Mg(x)Nb(y)N, y doped HfO2, where x includes one of: Al, Ca, Ce,Dy, Er, Gd, Ge, La, Sc, Si, Sr, Sn, or Y, wherein ‘x’ is a fraction;Niobate type compounds LiNbO3, LiTaO3, Lithium iron Tantalum OxyFluoride, Barium Strontium Niobate, Sodium Barium Niobate, or Potassiumstrontium niobate; or an improper ferroelectric which includes one of:[PTO/STO]n or [LAO/STO]n, where ‘n’ is between 1 to
 100. 17. A systemcomprising: a processor circuitry to execute one or more instructions; acommunication interface communicatively coupled to the processorcircuitry; and a memory coupled to the processor circuitry, wherein theprocessor circuitry comprises an AND-OR-inverter logic which includes: aAND logic gate comprising first three non-linear capacitors and aninverter; and an NOR logic gate comprising second three non-linearcapacitors, wherein an output of the AND logic gate is provided as inputto the NOR logic gate, and wherein an output of the NOR logic gate is anAND-OR-INVERT (AOI) logic function.
 18. The system of claim 17, whereinthe AND logic gate comprises: a first capacitor to receive a firstinput, the first capacitor coupled to a first node; a second capacitorto receive a second input, the second capacitor coupled to the firstnode; and a third capacitor to receive a third input, wherein the firstcapacitor, the third capacitor are coupled to the first node; whereinthe first three non-linear capacitors include the first capacitor, thesecond capacitor, and the third capacitor.
 19. The system of claim 18,wherein the NOR logic gate includes: a fourth capacitor to receive afourth input, the fourth capacitor coupled to a second node; a fifthcapacitor to receive the output of the AND logic gate, the fifthcapacitor coupled to the second node; a sixth capacitor to receive afifth input, wherein the sixth capacitor is coupled to the second node,wherein the second three non-linear capacitors include the fourthcapacitor, the fifth capacitor, and the sixth capacitor; and an inverterhaving an input coupled to the second node, wherein an output of theinverter is the AOI logic function.
 20. The system of claim 19, whereinthe third input is coupled to a ground node, and wherein the fifth inputis coupled to a supply node.